Towards sub-nanometer real-space observation of spin and orbital magnetism at the Fe/MgO interface

While the performance of magnetic tunnel junctions based on metal/oxide interfaces is determined by hybridization, charge transfer, and magnetic properties at the interface, there are currently only limited experimental techniques with sufficient spatial resolution to directly observe these effects simultaneously in real-space. In this letter, we demonstrate an experimental method based on Electron Magnetic Circular Dichroism (EMCD) that will allow researchers to simultaneously map magnetic transitions and valency in real-space over interfacial cross-sections with sub-nanometer spatial resolution. We apply this method to an Fe/MgO bilayer system, observing a significant enhancement in the orbital to spin moment ratio that is strongly localized to the interfacial region. Through the use of first-principles calculations, multivariate statistical analysis, and Electron Energy-Loss Spectroscopy (EELS), we explore the extent to which this enhancement can be attributed to emergent magnetism due to structural confinement at the interface. We conclude that this method has the potential to directly visualize spin and orbital moments at buried interfaces in magnetic systems with unprecedented spatial resolution.

The structure of the Fe/MgO interface grown for this study was investigated through the use of HRTEM, and the results of this are shown in gure 1. In gure 1a, the sample was tilted to a two-beam condition with g = (1 1 0) Fe . Vertical streaks within the iron lm are the consequence of a Moiré contrast generated between the cladding oxide layers and the metallic underlayer, and is discussed in greater detail in the supplementary information of [1]. At the interface, however, an alternating contrast bowing upwards into the Fe lm can be observed. This is likely due to local alterations of the crystallographic symmetry due to mist dislocations in this region. The spacing of these mist dislocations is approximately 4 nm, consistent with previous reports [2]. In gure 1b, a HRTEM micrograph of the interface is presented. The defocus value in this image is close to Gaussian defocus. Below, the modulus of three Fourier transforms from the regions denoted are presented. The presence of MgO and metallic iron can be inferred from the reections visible in the substrate and lm regions, respectively. However, the Fourier transform from the interfacial region (denoted as the region with an additional horizontal frequency) appears to contain both Fe and MgO reections. Moreover, an additional reection, denoted with the yellow arrows, appears in the FFT. This reection ts well with the kinematically-forbidden MgO (0 0 1) reection, and has been observed previously as well [3]. It is suspected that this arises from surface roughness on the MgO and the three-dimensional growth of the subsequent Fe layer, which is thus oset by half of an MgO unit cell in the growth direction for several nanometers [4].

FIG. 2.
Two HRTEM micrographs from dierent sample regions revealing large surface steps in the MgO substrate that propagate into the iron thin lm region. The lateral distance over which the interface is suspected to be projected is estimated to lie between the dashed yellow lines.
Direct observations of such steps are presented in gure 2. Two independent regions of the sample were investigated where perturbations of the MgO surface were suspected to arise. These HRTEM images were acquired on a C S -corrected ARM TEM (JEOL company) at Nagoya University, Nagoya, Japan. The steps disturb the subsequent iron growth along the direction of the electron beam propagation, leading to the Moiré contrast observed in gure 1b. The height of the steps can be estimated in these images since the MgO step appears to have extended through most of the TEM lamella in this region. We observe that the disturbed region is on the order of 5 nm, suggesting that the projection of the interface also extends over this distance for the EMCD experiments. Signicantly, these HRTEM investigations reveal no clear evidence for the formation of a secondary phase at this interface, further supporting the interpretation that the oxide signal observed in the 3 EELS data comes from the direct bond between the bulk iron atoms and the oxygen atoms within the MgO substrate itself. Hence, we conclude that the interfacially-bonded iron atoms are projected over a length of some nanometers, resulting in what appears to be an extended interfacial region, similar to the conclusions of Serin et al. [3]. The chemistry of the interface from a dierent region was investigated using EELS on a probe C S corrected TEM (JEOL, Inc.) at Nagoya University, Japan. At the top of gure 3, the HAADF survey image is provided and the vacuum, lm, and MgO regions are labeled.

Fe film MgO Vacuum
A spectrum image from this region was acquired and the resulting datacube was vertically summed into a line scan across the region shown. The integrated intensities of the iron and magnesium post edge regions are plotted on the same x-axis as the HAADF image. For the oxygen prole, the pre-peak was integrated rather than the post-edge region allowing for a qualitative segregation of iron oxide from the oxygen in the MgO substrate [5]. These proles are scaled to t a common range to visualize the qualitative trends across the bilayer.
The white-line ratio of the iron was extracted using the technique outlined in [3,6] and is presented in absolute units appearing on the y-axis.
The reduction of the Mg signal provides some insight into the extent of the projection of the atomic steps into the iron layer as well as the inuence of beam broadening due to the large convergence angle (30 mrad), similar to prior studies showing similar dechanneling behavior [2,3]. Beyond this broadening, there is no evidence for interdiusion of Mg. Over the same length scale, a strong increase in the iron white-line ratio is observed, once again consistent with previous investigations [2,3]. The white line ratio change is known to be related to an increase in the oxidation state of iron [5] and is accompanied by an increase in the intensity of the oxygen pre-peak, clearly indicating that the iron in the interfacial proximity is bonded with oxygen in some manner.

PRESENTATION OF THE RAW EMCD SPECTRA
The raw EMCD data are presented in gure 4. The pre-treatment steps described in the methods section of the manuscript were applied to these data; they otherwise were untreated before this stage. The spectra here were generated by summing the data over two dierent regions: the entire spectrum image (full) and the three columns at the interface (interface). This technique has been shown in a previous study to dramatically improve the signal to noise ratio of the EMCD spectra, at the cost of reduced spatial resolution [1].
The raw, untreated spectra are shown for these two summations in gure 4a and d. The pre-edge background model and its extrapolation is also presented. This background was subsequently subtracted and the spectra were normalized to the post-edge region shown in gure 4b and e. At bottom of each of these graphs, the dierence between the two spectra is shown. This is the EMCD signal of interest.    Since the low-loss spectra for this lamella were recorded to allow for the removal of plural scattering events from the EMCD data, it is also possible to calculate the thickness of the lamella on a pixel-by-pixel basis. This is performed in gure 6. Throughout the bulk of the lamella, the thickness remains relatively constant at around 0.68 ± 0.06 mean free paths.
The reduction on the right side of the image is partially caused by the overlap of the MgO interface with the Fe thin lm. A calculation of the absolute thickness of the iron layer is complicated by this overlap, which takes place together with the cladding oxide layers.
The thickness of these oxide layers can only be determined in combination with a structural investigation that yields a reasonable assumption for the structure and density of the oxide layers.

OXYGEN PRE-PEAK INTEGRATION WINDOW
Key to understanding the chemical behavior at the interface is the observation of the oxygen K-edge in the EELS data. This edge is well documented for both iron oxide compounds as well as for MgO. The oxygen pre-peak is observed at an energy loss that is signicantly lower than the oxygen edge for MgO, providing a way to segregate the two signals. This allows for a statement about the presence of oxidized iron at the interface, be it either due to edge from the MgO and the iron oxide is apparent and is suciently large for this analysis to distinguish. An additional important observation is that the onset position of the prepeak appears to shift to higher energy loss close to the interface. This is most apparent in the Moiré spectrum but is also evident at the interface, where the pre-peak appears as a shoulder superimposed over the MgO edge. This shift cannot be explained by instrumental energy drift, as all spectra were aligned to the Fe L 3 edge. Moreover, each one of these spectra represents a summation over 60 individual spectra. Hence the energy shift must be a physically relevant eect related to chemical shifts.
The shifting of the oxygen pre-peak complicates the placement of the integration window is placed close to the onset of the MgO oxygen edge, then a large increase in the oxygen concentration is observed that is unlikely to be caused by the presence of an iron oxide. This increase extends away from the interface into the iron lm by a signicant amount and may lead to the false conclusion that there is an additional oxide layer present at the interface.
However, if the window is placed at a lower energy loss such as 532 eV, then the pre-peak belonging to iron oxide is successfully segregated from the MgO, and no additional increase of oxygen is observed at the interface. The oxygen pre-peak is known to originate from the contaminating oxide layers that grow on the iron surface, and this result indicates that the amount and, hence, thickness of these layers remains invariant as one moves closer to the Fe / MgO interface.
A more detailed analysis of the oxygen chemistry of the interface was carried out by using multiple linear least-squares (MLLS) tting of the experimental spectra to reference spectra. Two reference spectra were used for the tting procedure: the surface oxide and the MgO spectra (see gure 8a). These two reference spectra were then linearly combined The STEM-EMCD experiment presented in the manuscript was designed to minimize beam damage to the sample as best as possible while still retaining a large enough signal to noise ratio in the raw spectra to allow for EMCD analysis. The concern is that the beam would decompose the MgO substrate between the Chiral Plus and Chiral Minus scans, thereby resulting in an articial increase in the white line ratio that could be misinterpreted as magnetic in origin. We stress here that we cannot completely rule out this eect with the present experimental design, and we have attempted to articulate this in the manuscript.
Nevertheless, we have taken the following eorts to minimize the chance that such an eect could take place.
First, the pixel dwell time was minimized to prevent excessive radiation dosage to the sample. This was accomplished by using a pixel dwell time of 0.2 s. The loss in signal was compensated for by collecting a large quantity of spectra (6000 for each datacube) and 13 increasing the collection angle. This improved the spatial resolution of the experiment but also reduced the angular sensitivity. Our ndings indicate that this is an acceptable tradeo to make, provided that the signal to noise level of an individual spectrum is suciently large for the variance of the EMCD signal to be captured by the subsequent multivariate statistical treatment.
Second, prior to the scan, raw spectra from neighboring regions were inspected to determine which aperture pairing yielded iron ionization edges with the highest white line ratio. Finally, the survey region was scanned both before and after the data acquisition to inspect for structural and z-contrast dierences. These scans are presented in gure 11.
Signicant variations were neither observed in the iron lm nor in the MgO substrate. The small dierences in contrast between the two images can be attributed to changes in the electron optical conditions arising from the reduction of the incident beam current necessary to acquire the low-loss spectrum image.

ROBUST PCA ANALYSIS
The raw datacubes were decomposed using robust PCA [7]. ARTIFICIAL SPATIAL SHIFTING OF m L /m S MAPS As discussed in the manuscript, one of the potential sources for systematic error in this experiment is a spatial drift that takes place between scans. The concern is that, if one scan contains a larger percentage of interfacial iron atoms than the second, then some part of the white line ratio change will be due to charge transfer rather than magnetism. This would be dicult to detect and disentangle from a magnetic eect and thus adds uncertainty to To understand this eect, we articially shifted the two datacubes with respect to one another. The result of this operation is presented in gure 16. These maps were generated by shifting the datacubes relative to each other in the direction perpendicular to the interface by between -4 to +4 pixels before applying the sum rules on a pixel-by-pixel basis. This was performed with the map reconstructions for three, four, and ve principal components.
We observe that, for very large shifts, some structure appears in the iron bulk. This likely corresponds to regions of the sample with dierent oxide contents being compared, and justies our more general concern that the probe position must be very accurate between scans for a pixel-by-pixel comparison to work. However, we also observe that these additional features tend to disappear at a shift of 0, implying that the drift correction routines were accurate to within one pixel. We further observe that, despite even very large shifts, the observed enhancement of m L /m S at the interface remains largely intact. We interpret this to arise from the relatively large spread of the white line ratio change over the interfacial region, due to the structurally rough nature of the interface as discussed in the manuscript.
Thus, we feel quite condent that large spatial drifts in excess of one pixel can be excluded as a cause for the m L /m S interfacial enhancement, and that sub-pixel drifts are insuciently strong to account for it on their own.

19
Number of PCA components Considering that the fourth component is shown to be important according to the scree plots, we have focused on the range from 4 to 7 principal components. Figure 18   The full-potential linearized augmented plane-wave method (FP-LAPW) as implemented in the WIEN2k code [9] is used for both the initial optimization of the structure and fol-   Only p-DOS is plotted, since this one is mainly responsible for the signal seen in the oxygen K-edge. The third layer of oxygens has a DOS very close to the bulk MgO. The rst layer, closest to the interface is rather dierent and the second layer shows features in between of the two, but closer to the bulk-like DOS. Therefore it appears that the modication of local electronic structure of oxygens due to interface is localized to the two closest atomic layers. Nevertheless, these two atomic layers provide a likely explanation for the appearance of residual oxygen K-edge signal in the t of the spectra reported in Fig. 10.
Qualitatively similar picture is also observed for the projected DOS of iron atoms. The

ESTIMATION OF SPATIAL RESOLUTION IN THE EXPERIMENT
We estimate computationally the spatial resolution of the STEM-EMCD reported in the main text. The initial probe broadens as it propagates and inside the crystal it also scatters, which can broaden it further.
An initial FWHM probe size for a 300 keV beam with convergence semi-angle α = 2.5 mrad is estimated to be 0.53 λ/α ≈ 4. broadening. This incoherence allows us to obtain an estimate of the probe broadening due to diraction eects just by passing a single diraction-limited probe through the crystal.
We have done simulations of the electron probe with a multislice method. The structure model was a large 148-atom orthogonal supercell of bcc-Fe with its c-axis oriented parallel to a zone axis (0, 7, 5), which corresponds to a direction tilted approximately 10 • from the (0, 1, 1) zone axis, representing a systematic-row conditions very close to the experimental ones. The incoming beam, with acceleration voltage and convergence angle set as in the experiment, was tilted to a two-beam condition with G = (2, 0, 0) by about 6.8 mrad in the x-direction. Figure 22 compares the initial probe (top left) and scattered probe (top right) and the averages of their intensities along the x, y-directions. The channeling of the 25 probe along the lattice planes is well visible as a periodic modulation of the probe along the x-direction. On the other hand, in the y-direction the probe shape is barely modied by the scattering. Overall, despite that the probe develops heavier tails due to the scattering, its FWHM remains practically the same even after passing through 100 nm of the crystal.
Although this nding might appear counter-intuitive, it is easy to explain qualitatively.
The depth of focus of a probe scales with inverse square of the convergence angle and it is approximately given by a formula 1.77 λ/α 2 , which for 300 keV beam and 2.5 mrad convergence semi-angle gives approximately 560 nm. Hence, it is expected that a probe with such small convergence angle stays in focus. Moreover, our simulations show that the scattering does not signicantly broaden the probe. The two-beam orientation of the crystal manifests itself in the probe only as a periodic intensity modication with periodicity of the lattice planes (channeling eect) and via an appearance of an asymmetric shoulder.
We conclude that the FWHM of the probe is not likely to broaden signicantly beyond its initial FWHM. Therefore the spatial resolution of the STEM-EMCD experiment should remain close to 8 Å, safely below one nanometer. * thomas.thersle@mmk.su.se; Present address: Stockholm University, Department of Materials and Environmental Chemistry (MMK), 10691 Stockholm, Sweden.